Question: The sum of $6$ consecutive even numbers is $102$. What is the sixth number in this sequence?
Call the first number in the sequence $x$ The next even number in the sequence is $x + 2$ The sum of the $6$ consecutive even numbers is: $x+ (x + 2)+ (x + 4)+ (x + 6)+ (x + 8)+ (x + 10) = 102$ $6x + 30= 102$ $6x = 72$ $x = 12$ Since $x$ is the first number, $x + 10$ is the sixth even number. Thus, the sixth number in the sequence is $22$.